(A) The satellite is moving in force-free space,so the only force acting on it is the retarding force due to the accretion of dust.According to Newton

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(A) The satellite is moving in force-free space,so the only force acting on it is the retarding force due to the accretion of dust.According to Newton's second law,the force $F$ is equal to the rate of change of momentum: $F = \frac{d p}{d t} = \frac{d}{d t}(Mv)$.Since the satellite is moving at speed $v$ and collecting mass at a rate $\frac{d M}{d t} = \alpha v$,the retarding force is $F = -v \frac{d M}{d t}$.Substituting the given rate of mass change: $F = -v (\alpha v) = -\alpha v^{2}$.Using $F = Ma$,we have $Ma = -\alpha v^{2}$.Therefore,the acceleration $a = \frac{-\alpha v^{2}}{M}$.

Class 11 Physics Newton's Laws of Motion and Friction Variable Mass System and Rocket Problem

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$A$ satellite in force-free space sweeps stationary interplanetary dust at a rate of $\frac{d M}{d t} = \alpha v$,where $M$ is the mass,$v$ is the speed of the satellite,and $\alpha$ is a constant. The acceleration of the satellite is:

A
$\frac{-\alpha v^{2}}{M}$
B
$-\alpha v^{2}$
C
$\frac{-2 \alpha v^{2}}{M}$
D
$\frac{-\alpha v^{2}}{2 M}$

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Newton's Laws of Motion and Friction

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Variable Mass System and Rocket Problem

$A$ solid disc of mass $M$ is held horizontally in the air by throwing $40$ stones per second vertically upwards to strike the disc,each with a velocity of $6\,m/s$. If the mass of each stone is $0.05\,kg$,what is the mass of the disc in $kg$? (Take $g = 10\,m/s^2$)

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$A$ rocket is fired upward from the earth's surface such that it creates an acceleration of $19.6 \,m/s^2$. If after $5 \,s$ its engine is switched off,the maximum height of the rocket from the earth's surface would be.........$m$

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$A$ heap of rope with mass density $\lambda$ (per unit length) lies on a table. You grab one end and pull horizontally with constant speed $v$,as shown in the figure. (Assume that the rope has no friction with itself in the heap.) The force that you must apply to maintain the constant speed $v$ is

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$A$ satellite in force-free space sweeps stationary interplanetary dust at a rate $\frac{dM}{dt} = \alpha v$,where $M$ is the mass,$v$ is the velocity of the satellite,and $\alpha$ is a constant. What is the deceleration of the satellite?

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$A$ balloon and its content having mass $M$ is moving up with an acceleration $a$. The mass that must be released from the content so that the balloon starts moving up with an acceleration $3a$ will be: (Take $g$ as acceleration due to gravity)

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$A$ satellite in force-free space sweeps stationary interplanetary dust at a rate of $\frac{d M}{d t} = \alpha v$,where $M$ is the mass,$v$ is the speed of the satellite,and $\alpha$ is a constant. The acceleration of the satellite is:

Similar Questions

$A$ solid disc of mass $M$ is held horizontally in the air by throwing $40$ stones per second vertically upwards to strike the disc,each with a velocity of $6\,m/s$. If the mass of each stone is $0.05\,kg$,what is the mass of the disc in $kg$? (Take $g = 10\,m/s^2$)

$A$ rocket is fired upward from the earth's surface such that it creates an acceleration of $19.6 \,m/s^2$. If after $5 \,s$ its engine is switched off,the maximum height of the rocket from the earth's surface would be.........$m$

$A$ heap of rope with mass density $\lambda$ (per unit length) lies on a table. You grab one end and pull horizontally with constant speed $v$,as shown in the figure. (Assume that the rope has no friction with itself in the heap.) The force that you must apply to maintain the constant speed $v$ is

$A$ satellite in force-free space sweeps stationary interplanetary dust at a rate $\frac{dM}{dt} = \alpha v$,where $M$ is the mass,$v$ is the velocity of the satellite,and $\alpha$ is a constant. What is the deceleration of the satellite?

$A$ balloon and its content having mass $M$ is moving up with an acceleration $a$. The mass that must be released from the content so that the balloon starts moving up with an acceleration $3a$ will be: (Take $g$ as acceleration due to gravity)

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